Problem: The sum of two angles is $72^\circ$. Angle 2 is $138^\circ$ smaller than $4$ times angle 1. What are the measures of the two angles in degrees?
Answer: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 72}$ ${y = 4x-138}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${4x-138}$ for $y$ in the first equation. ${x + }{(4x-138)}{= 72}$ Simplify and solve for $x$ $ x+4x - 138 = 72 $ $ 5x-138 = 72 $ $ 5x = 210 $ $ x = \dfrac{210}{5} $ ${x = 42}$ Now that you know ${x = 42}$ , plug it back into $ {y = 4x-138}$ to find $y$ ${y = 4}{(42)}{ - 138}$ $y = 168 - 138$ ${y = 30}$ You can also plug ${x = 42}$ into $ {x+y = 72}$ and get the same answer for $y$ ${(42)}{ + y = 72}$ ${y = 30}$ The measure of angle 1 is $42^\circ$ and the measure of angle 2 is $30^\circ$.